"Next of Kin" has no function in law, Kassee and will certainly not determine who would receive your son's assets in the event of his death. You can nominate anybody as your "next of kin" though why you should choose to do so is not very obvious as it means very little.
The info you have been given should enable you to establish that (if I'm correct and you live in England or Wales) your son's estate would be divided equally between you and your ex. If you're in Scotland and you have other children half his estate will go to you and your ex (shared equally) and the other half to his siblings (in equal shares). Slightly more complex rules exist for Northern Ireland.
If he wants anything else to happen he should make a will.